Mathematical modelling of an aqueous electrolyte solution by incorporating the variation of dielectric constant

Abstract

The important lapse in the failure of Debye-Huckel theory was established during the last century by detailed theoretical and experimental work of Glueckauff, Pitzer, Buchner, Barthel and the Nobel newlinePrize winners Eigen and Tamm. The omission of incorporation of dielectric permittivity variation with concentration is attributed to be sole cause for several interesting mechanisms observed in electrolytic solutions. This dissertation developed a model to fill the void. A nonlinear equation for Dielectric constant as a function of three different powers of newlineconcentration was proposed. Gauss-Newton method was used in curve fitting the Dielectric data. The Poisson-Boltzmann equation provided access to apply the proposed correction to the Debye-Huckel theory. The governing equations for an electro-osmatic flow of an aqueous electrolyte solution were developed by fully coupled Navier Stokes, Maxwell newlineStefan, Poisson - Boltzmann equations. The Finite difference method and Finite element method were used to solve the governing equations. All through the work advanced computational technique of MATLAB was used. The results of the model used in the governing equations for the potential and other related parameters were presented as one and two dimensional plots drawn with the help of MATLAB. A critical analysis of these plots was presented. An excellent agreement was found between this theory and related results. The possible scope for extension of this model in future work is given. newline